This time, two, not one

I konw you guys have solve so many problems about increasing sequence, this time, a little change has been made.
Assume that there is a sequence S = {s1, s2, s3, ..., sn}, si = (xi, yi).You should find two increasing subsequence L1 and L2, and they have no common elements, means L1∩L2 = φ, and the sum of their lenth is as max as possible.
Here we assume si > sj is that (xi > xj && yi > yj) or (xi >= xj && yi > yj) or (xi > xj && yi >= yj). I will ensure that all elements' coordinates are distinct, i.e., si != sj (i!=j).

The input consists of multiple test cases. Each case begins with a line containing a positive integer n that is the length of the sequence S, the next n lines each contains a pair integers (xi, yi), i = 1,...n.1 <= n <= 5000,1<=xi,yi<=2^31.

For each test case, output one line containing the the maximum sum of the two increasing subsequence L1 and L2 you can find.

3
1 3
3 1
2 2
4
1 2
2 1
4 3
3 4

2
4

Hint: In the second case, you can make L1 = {(1,2), (3,4)} and L2 = {(2,1), (4,3)}, or L1 = {(1,2), (4,3)} and L2 = {(2,1), (3,4)}.

8600